If `Delta_r =|[2^(r-1) ,2.3^(r-1), 4.5^(r-1)],[alpha,beta,gamma],[2^n-1, 3^n-1, 5^n-1]|` , then find the value of `Delta`

If Delta_(r)=det[[2^(r-1),2.3^(r-1),4.5^(r-1)alpha,beta,gamma2^(n)-1,3^(n)-1,5^(n)-1]], then find

If D_r= |[2^r-1,2 . 3^(r-1), 4 . 5^(r-1)],[alpha ,beta, gamma],[2^(n-1),3^(n-1),5^(n-1)]| then sum_(r=1)^n D_r=

If Delta_r=|[2^(r-1) , 2.3^(r-1) , 4. 5^(r-1)] , [x , y , z] , [2^n-1 , 3^n-1 , 5^n-1]|dot Show that sum_(r=1)^n Delta_r=Con s t a n t

If Delta_r=|[2^(r-1)2 , 3^(r-1) , 4. 5^(r-1)] , [x , y , z] , [2^n-1 , 3^n-1 , 5^n-1]|dot Show that sum_(r=1)^n Delta_r=Con s t a n t

If "Delta"_r=|[2^(r-1),2. 3^(r-1),4. 5^(r-1)],[x, y ,z],[2^n-1, 3^n-1, 5^n-1]| Show that sum_(r=1)^n"Delta"_r = Constant

Let Delta_(r)=|(2^(r-1),2(3^(r-1)),4(5^(r-1))),(alpha, beta, gamma),(2^(n)-1,3^(n)-1,5^(n)-1)| for r=1,2,………..n . The sum_(r=1)Delta_(r) is

If D_(r)=|(2^(r-1),2(3^(r-1)),4(5^(4-1))),(x,y,z),(2^(n)-1,3^(n)-1,5^(n)-1)| then sum_(r=1)^(n)D_(r)=